She could leave it on her desk.
That would violate the law:
The Council will select two or more nominees to send to the governor. The governor will have 45 days to make an appointment from the Council's list.
The governor appoints a supreme court justice or a judge of the court of appeals, superior court, or district court from a list of qualified candidates submitted by the Alaska Judicial Council. The governor has 45 days from receipt of the list to make the appointment.
The names of Superior Court Judges Morgan Christen and Eric Smith were forwarded to Gov. Sarah Palin, who by law has 45 days to appoint one of them to Alaska's highest court.